Hands-on math!

Inscribed figure

An inscribed figure is one that is drawn
inside another, usually with the edges touching, like this:

In the above example the square is inscribed in the circle.

A common problem with inscribed figures
is to find the area of the shaded area in the above figure.
That's the area of the circle that is not inside the square.
That area is the area of the circle minus the area of the square.

So, if AB = 10 inches and
R = OD = 7.07 inches (the circle's radius),
then the shaded area is:

A = circle's area - square's area
A = (R2) -         10*10
A = 157.03 -         100     = 57.03 sq. in.